(i) To find the \(x\)-coordinate of \(A\), set \(\sin x = 2 \cos x\).

This implies \(\tan x = 2\).

Solving for \(x\), we find \(x = 1.11\) (or approximately \(0.352\pi\)).

(ii) For the \(y\)-coordinate of \(B\), we need the value of \(y\) when \(x\) is such that \(y = \sin x = 2 \cos x\) and \(y < 0\).

The negative solution for \(y\) is in the range \(-1 < y < -0.8\).

The value is approximately \(y = -0.895\).